Numerical simulation of singularly perturbed non-linear elliptic boundary value problems using finite element method
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摘要
The present paper presents the finite element solution of two-dimensional non-linear singularly perturbed elliptic partial differential equation subject to appropriate Dirichlet boundary conditions. A new fifth order convergent Newton type iterative method has been described and used to linearize the non-linear problem. The inclusion of this Newton’s method of fifth order convergence in finite element method for solving non-linear system of equations reduces the number of iterations and hence the cost of computation. To demonstrate the usefulness of the proposed scheme, a non-convex variational Ginzburg–Landau equation is considered.
论文关键词:Singular perturbation,Elliptic boundary value problem,Finite element method,Newton’s method,Ginzburg–Landau equation
论文评审过程:Available online 15 July 2012.
论文官网地址:https://doi.org/10.1016/j.amc.2012.06.011